Question

simplificando os radicais :1\2√300=?

Answer 1

$\dfrac{1}{2 \sqrt{300}}$

Fatorar 300

300 | 2
150 | 2
  75 | 3
  25 | 5
    5 | 5
    1 | == 2² . 3 . 5²

√300 = √2² . 3 . 5²

===
$\dfrac{1}{2 \sqrt{300}} \\ \\ \\ \dfrac{1}{2 \sqrt{2^2 . 3 . 5^2}} \\ \\ \\ \dfrac{1}{2 . 2 . 5\sqrt{ 3}} \\ \\ \\ \dfrac{1}{2 . 10\sqrt{ 3}} \\ \\ \\ \dfrac{1}{20\sqrt{ 3}} \\ \\ \\ \dfrac{1 . 20\sqrt{ 3}}{(20\sqrt{ 3}) . (20\sqrt{ 3})} \\ \\ \\ \dfrac{20\sqrt{ 3}}{(20\sqrt{ 3})^2} \\ \\ \\ \dfrac{20\sqrt{ 3}}{400 . 3} \\ \\ \\ \dfrac{20\sqrt{ 3}}{1200} \\ \\ \\ =\ \textgreater \ \dfrac{\sqrt{ 3}}{60}$

Answer 2

$\frac{1}{2 \sqrt{300} } = \frac{1}{2 \sqrt{3\cdot100} }= \frac{1}{2 \sqrt{100}\cdot\sqrt{3} }= \frac{1}{2 \cdot10\cdot\sqrt{3} } = \frac{1}{20\cdot\sqrt{3} } \\ \\= \frac{1}{20\cdot\sqrt{3} }\cdot \frac{\sqrt{3}}{ \sqrt{3}} = \frac{ \sqrt{3}}{20\cdot\sqrt{9}} =\frac{ \sqrt{3}}{20\cdot3} =\frac{\sqrt{3}}{60}$